Mostowski Quantifier

	Mostowski Quantifier Mostowski (feminine: Mostowska, plural: Mostowscy) is a surname. It may refer to: * Mostowski Palace ( pl, Pałac Mostowskich), an 18th-century palace in Warsaw * Andrzej Mostowski (1913 - 1975), a Polish mathematician Mostowski collapse lemma, in mathematical logic Ehrenfeucht–Mostowski theorem, in model theory ** Mostowski model In mathematical set theory, the Mostowski model is a model of set theory with atoms where the full axiom of choice fails, but every set can be linearly ordered. It was introduced by . The Mostowski model can be constructed as the permutation mode ... in set theory See also * Mostovsky {{surname, Mostowski, Mostowsky, Mostowska, etc. Polish-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Mostowski Palace Mostowski Palace ( pl, Pałac Mostowskich) is an 18th-century palace in Warsaw, Poland, located at ''ul. Nowolipie 2'' (2 Nowolipie Street) — prior to World War II, at ''ul. Przejazd 15''. History The palace had been built in 1762-65 in the Baroque style for the Voivode of Minsk, . In 1795 it became, by inheritance, the property of Tadeusz Mostowski, a prominent figure of revolutionary Poland. The palace was purchased by the government and rebuilt in 1823-24 in the classicist style to a design by Antonio Corazzi. The building became the seat of Congress Poland's Commission of Internal Affairs and Police, and a venue of concerts by Fryderyk Chopin. In 1831 the palace was taken over for the needs of the Russian Army. Renovated in 1920, it became the seat of various municipal offices. During World War II, in 1944, it was destroyed by the Germans, except for the facade. After the war, in 1949, the Mostowski Palace was rebuilt. It is now the seat of Warsaw's police headquarters. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Andrzej Mostowski Andrzej Mostowski (1 November 1913 – 22 August 1975) was a Polish mathematician. He is perhaps best remembered for the Mostowski collapse lemma. Biography Born in Lemberg, Austria-Hungary, Mostowski entered University of Warsaw in 1931. He was influenced by Kuratowski, Lindenbaum, and Tarski. His Ph.D. came in 1939, officially directed by Kuratowski but in practice directed by Tarski who was a young lecturer at that time. He became an accountant after the German invasion of Poland but continued working in the Underground Warsaw University. After the Warsaw uprising of 1944, the Nazis tried to put him in a concentration camp. With the help of some Polish nurses, he escaped to a hospital, choosing to take bread with him rather than his notebook containing his research. Some of this research he reconstructed after the War, however much of it remained lost. His work was largely on recursion theory and undecidability. From 1946 until his death in Vancouver, British Columbia, Ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Mostowski Collapse Lemma In mathematical logic, the Mostowski collapse lemma, also known as the Shepherdson–Mostowski collapse, is a theorem of set theory introduced by and . Statement Suppose that ''R'' is a binary relation on a class ''X'' such that ''R'' is set-like: ''R''−1 'x''= is a set for every ''x'', ''R'' is well-founded: every nonempty subset ''S'' of ''X'' contains an ''R''-minimal element (i.e. an element ''x'' ∈ ''S'' such that ''R''−1 'x''∩ ''S'' is empty), ''R'' is extensional: ''R''−1 'x''≠ ''R''−1 'y''for every distinct elements ''x'' and ''y'' of ''X'' The Mostowski collapse lemma states that for every such ''R'' there exists a unique transitive class (possibly proper) whose structure under the membership relation is isomorphic to (''X'', ''R''), and the isomorphism is unique. The isomorphism maps each element ''x'' of ''X'' to the set of images of elements ''y'' of ''X'' such that ''y R x'' (Jech 2003:69). Generalizations Every well-founded set-like relation ... [...More Info...] [...Related Items...] OR:* [Wikipedia] [Google] [Baidu]
	Ehrenfeucht–Mostowski Theorem In model theory, a field within mathematical logic, the Ehrenfeucht–Mostowski theorem gives conditions for the existence of a model with indiscernibles. Statement A linearly ordered set ''X'' is called a set of indiscernibles of a model if the truth of a statement about elements of ''X'' depends only on their order. The Ehrenfeucht–Mostowski theorem states that if ''T'' is a theory with an infinite model, then there is a model of ''T'' containing any given linearly ordered set ''X'' as a set of indiscernibles. The proof uses Ramsey's theorem. Applications The Ehrenfeucht–Mostowski is used to construct models with many automorphisms. It is also used in the theory of zero sharp to construct indiscernibles in the constructible universe In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted by , is a particular class of sets that can be described entirely in terms of simpler sets. is the union of the constructible hierarchy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Mostowski Model In mathematical set theory, the Mostowski model is a model of set theory with atoms where the full axiom of choice fails, but every set can be linearly ordered. It was introduced by . The Mostowski model can be constructed as the permutation model corresponding to the group of all automorphisms of the ordered set of rational numbers In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all rationa ... and the ideal of finite subsets of the rational numbers. References * Set theory {{math-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Mostovsky Mostovsky (russian: Мостовский) or Mostovskoy (; both masculine), Mostovskaya (; feminine), or Mostovskoye (; neuter) is the name of several inhabited localities in Russia. ;Urban localities Mostovskoy, Krasnodar Krai, an urban-type settlement in Mostovsky District of Krasnodar Krai ;Rural localities Mostovskoy, Tula Oblast, a settlement in Shevelevskaya Rural Administration of Shchyokinsky District of Tula Oblast * Mostovsky, Volgograd Oblast, a ''khutor'' in Tryasinovsky Selsoviet of Serafimovichsky District of Volgograd Oblast * Mostovskoye, Krasnoyarsk Krai, a village in Mezhovsky Selsoviet of Bolshemurtinsky District of Krasnoyarsk Krai * Mostovskoye, Shatrovsky District, Kurgan Oblast, a '' selo'' in Mostovsky Selsoviet of Shatrovsky District of Kurgan Oblast * Mostovskoye, Vargashinsky District, Kurgan Oblast, a ''selo'' in Mostovskoy Selsoviet of Vargashinsky District of Kurgan Oblast * Mostovskoye, Moscow Oblast, a village in Ryazanovskoye Rural Settlemen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Mostowsky Mostowski (feminine: Mostowska, plural: Mostowscy) is a surname. It may refer to: * Mostowski Palace ( pl, Pałac Mostowskich), an 18th-century palace in Warsaw * Andrzej Mostowski (1913 - 1975), a Polish mathematician Mostowski collapse lemma, in mathematical logic Ehrenfeucht–Mostowski theorem, in model theory ** Mostowski model In mathematical set theory, the Mostowski model is a model of set theory with atoms where the full axiom of choice fails, but every set can be linearly ordered. It was introduced by . The Mostowski model can be constructed as the permutation mode ... in set theory See also * Mostovsky {{surname, Mostowski, Mostowsky, Mostowska, etc. Polish-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Mostowska Mostowski (feminine: Mostowska, plural: Mostowscy) is a surname. It may refer to: * Mostowski Palace ( pl, Pałac Mostowskich), an 18th-century palace in Warsaw * Andrzej Mostowski (1913 - 1975), a Polish mathematician Mostowski collapse lemma, in mathematical logic Ehrenfeucht–Mostowski theorem, in model theory ** Mostowski model in set theory See also * Mostovsky {{surname, Mostowski, Mostowsky Mostowski (feminine: Mostowska, plural: Mostowscy) is a surname. It may refer to: * Mostowski Palace ( pl, Pałac Mostowskich), an 18th-century palace in Warsaw * Andrzej Mostowski (1913 - 1975), a Polish mathematician Mostowski collapse lemma, ..., Mostowska, etc. Polish-language surnames ... [...More Info...] [...Related Items...] OR:** [Wikipedia] [Google] [Baidu]

	Mostowski Quantifier Mostowski (feminine: Mostowska, plural: Mostowscy) is a surname. It may refer to: * Mostowski Palace ( pl, Pałac Mostowskich), an 18th-century palace in Warsaw * Andrzej Mostowski (1913 - 1975), a Polish mathematician Mostowski collapse lemma, in mathematical logic Ehrenfeucht–Mostowski theorem, in model theory ** Mostowski model In mathematical set theory, the Mostowski model is a model of set theory with atoms where the full axiom of choice fails, but every set can be linearly ordered. It was introduced by . The Mostowski model can be constructed as the permutation mode ... in set theory See also * Mostovsky {{surname, Mostowski, Mostowsky, Mostowska, etc. Polish-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Mostowski Palace Mostowski Palace ( pl, Pałac Mostowskich) is an 18th-century palace in Warsaw, Poland, located at ''ul. Nowolipie 2'' (2 Nowolipie Street) — prior to World War II, at ''ul. Przejazd 15''. History The palace had been built in 1762-65 in the Baroque style for the Voivode of Minsk, . In 1795 it became, by inheritance, the property of Tadeusz Mostowski, a prominent figure of revolutionary Poland. The palace was purchased by the government and rebuilt in 1823-24 in the classicist style to a design by Antonio Corazzi. The building became the seat of Congress Poland's Commission of Internal Affairs and Police, and a venue of concerts by Fryderyk Chopin. In 1831 the palace was taken over for the needs of the Russian Army. Renovated in 1920, it became the seat of various municipal offices. During World War II, in 1944, it was destroyed by the Germans, except for the facade. After the war, in 1949, the Mostowski Palace was rebuilt. It is now the seat of Warsaw's police headquarters. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Andrzej Mostowski Andrzej Mostowski (1 November 1913 – 22 August 1975) was a Polish mathematician. He is perhaps best remembered for the Mostowski collapse lemma. Biography Born in Lemberg, Austria-Hungary, Mostowski entered University of Warsaw in 1931. He was influenced by Kuratowski, Lindenbaum, and Tarski. His Ph.D. came in 1939, officially directed by Kuratowski but in practice directed by Tarski who was a young lecturer at that time. He became an accountant after the German invasion of Poland but continued working in the Underground Warsaw University. After the Warsaw uprising of 1944, the Nazis tried to put him in a concentration camp. With the help of some Polish nurses, he escaped to a hospital, choosing to take bread with him rather than his notebook containing his research. Some of this research he reconstructed after the War, however much of it remained lost. His work was largely on recursion theory and undecidability. From 1946 until his death in Vancouver, British Columbia, Ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Mostowski Collapse Lemma In mathematical logic, the Mostowski collapse lemma, also known as the Shepherdson–Mostowski collapse, is a theorem of set theory introduced by and . Statement Suppose that ''R'' is a binary relation on a class ''X'' such that ''R'' is set-like: ''R''−1 'x''= is a set for every ''x'', ''R'' is well-founded: every nonempty subset ''S'' of ''X'' contains an ''R''-minimal element (i.e. an element ''x'' ∈ ''S'' such that ''R''−1 'x''∩ ''S'' is empty), ''R'' is extensional: ''R''−1 'x''≠ ''R''−1 'y''for every distinct elements ''x'' and ''y'' of ''X'' The Mostowski collapse lemma states that for every such ''R'' there exists a unique transitive class (possibly proper) whose structure under the membership relation is isomorphic to (''X'', ''R''), and the isomorphism is unique. The isomorphism maps each element ''x'' of ''X'' to the set of images of elements ''y'' of ''X'' such that ''y R x'' (Jech 2003:69). Generalizations Every well-founded set-like relation ... [...More Info...] [...Related Items...] OR:* [Wikipedia] [Google] [Baidu]
	Ehrenfeucht–Mostowski Theorem In model theory, a field within mathematical logic, the Ehrenfeucht–Mostowski theorem gives conditions for the existence of a model with indiscernibles. Statement A linearly ordered set ''X'' is called a set of indiscernibles of a model if the truth of a statement about elements of ''X'' depends only on their order. The Ehrenfeucht–Mostowski theorem states that if ''T'' is a theory with an infinite model, then there is a model of ''T'' containing any given linearly ordered set ''X'' as a set of indiscernibles. The proof uses Ramsey's theorem. Applications The Ehrenfeucht–Mostowski is used to construct models with many automorphisms. It is also used in the theory of zero sharp to construct indiscernibles in the constructible universe In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted by , is a particular class of sets that can be described entirely in terms of simpler sets. is the union of the constructible hierarchy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Mostowski Model In mathematical set theory, the Mostowski model is a model of set theory with atoms where the full axiom of choice fails, but every set can be linearly ordered. It was introduced by . The Mostowski model can be constructed as the permutation model corresponding to the group of all automorphisms of the ordered set of rational numbers In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all rationa ... and the ideal of finite subsets of the rational numbers. References * Set theory {{math-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Mostovsky Mostovsky (russian: Мостовский) or Mostovskoy (; both masculine), Mostovskaya (; feminine), or Mostovskoye (; neuter) is the name of several inhabited localities in Russia. ;Urban localities Mostovskoy, Krasnodar Krai, an urban-type settlement in Mostovsky District of Krasnodar Krai ;Rural localities Mostovskoy, Tula Oblast, a settlement in Shevelevskaya Rural Administration of Shchyokinsky District of Tula Oblast * Mostovsky, Volgograd Oblast, a ''khutor'' in Tryasinovsky Selsoviet of Serafimovichsky District of Volgograd Oblast * Mostovskoye, Krasnoyarsk Krai, a village in Mezhovsky Selsoviet of Bolshemurtinsky District of Krasnoyarsk Krai * Mostovskoye, Shatrovsky District, Kurgan Oblast, a '' selo'' in Mostovsky Selsoviet of Shatrovsky District of Kurgan Oblast * Mostovskoye, Vargashinsky District, Kurgan Oblast, a ''selo'' in Mostovskoy Selsoviet of Vargashinsky District of Kurgan Oblast * Mostovskoye, Moscow Oblast, a village in Ryazanovskoye Rural Settlemen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Mostowsky Mostowski (feminine: Mostowska, plural: Mostowscy) is a surname. It may refer to: * Mostowski Palace ( pl, Pałac Mostowskich), an 18th-century palace in Warsaw * Andrzej Mostowski (1913 - 1975), a Polish mathematician Mostowski collapse lemma, in mathematical logic Ehrenfeucht–Mostowski theorem, in model theory ** Mostowski model In mathematical set theory, the Mostowski model is a model of set theory with atoms where the full axiom of choice fails, but every set can be linearly ordered. It was introduced by . The Mostowski model can be constructed as the permutation mode ... in set theory See also * Mostovsky {{surname, Mostowski, Mostowsky, Mostowska, etc. Polish-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Mostowska Mostowski (feminine: Mostowska, plural: Mostowscy) is a surname. It may refer to: * Mostowski Palace ( pl, Pałac Mostowskich), an 18th-century palace in Warsaw * Andrzej Mostowski (1913 - 1975), a Polish mathematician Mostowski collapse lemma, in mathematical logic Ehrenfeucht–Mostowski theorem, in model theory ** Mostowski model in set theory See also * Mostovsky {{surname, Mostowski, Mostowsky Mostowski (feminine: Mostowska, plural: Mostowscy) is a surname. It may refer to: * Mostowski Palace ( pl, Pałac Mostowskich), an 18th-century palace in Warsaw * Andrzej Mostowski (1913 - 1975), a Polish mathematician Mostowski collapse lemma, ..., Mostowska, etc. Polish-language surnames ... [...More Info...] [...Related Items...] OR:** [Wikipedia] [Google] [Baidu]