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Hrushovski Construction
In model theory, a branch of mathematical logic, the Hrushovski construction generalizes the Fraïssé limit In mathematical logic, specifically in the discipline of model theory, the Fraïssé limit (also called the Fraïssé construction or Fraïssé amalgamation) is a method used to construct (infinite) mathematical structures from their (finite) su ... by working with a notion of ''strong substructure'' \leq rather than \subseteq. It can be thought of as a kind of "model-theoretic forcing", where a (usually) stable structure is created, called the ''generic'' or ''rich'' model. The specifics of \leq determine various properties of the generic, with its geometric properties being of particular interest. It was initially used by Ehud Hrushovski to generate a stable structure with an "exotic" geometry, thereby refuting Zil'ber's Conjecture. Three conjectures The initial applications of the Hrushovski construction refuted two conjectures and answered a third question in the n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Theory
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold). The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself. In particular, model theorists also investigate the sets that can be defined in a model of a theory, and the relationship of such definable sets to each other. As a separate discipline, model theory goes back to Alfred Tarski, who first used the term "Theory of Models" in publication in 1954. Since the 1970s, the subject has been shaped decisively by Saharon Shelah's stability theory. Compared to other areas of mathematical logic such as proof theory, model theory is often less concerned with formal rigour and closer in spirit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Logic
Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and Mathematical analysis, analysis. In the early 20th century it was shaped by David Hilbert's Hilbert's program, program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Age (model Theory)
Age or AGE may refer to: Time and its effects * Age, the amount of time someone or something has been Life, alive or has existed ** East Asian age reckoning, an Asian system of marking age starting at 1 * Ageing or aging, the process of becoming old age, older ** Senescence, the gradual deterioration of biological function with age ** Human development (biology) * Periodization, the process of categorizing the past into discrete named blocks of time ** Ages of Man, the stages of human existence on the Earth according to Greek mythology and its subsequent Roman interpretation **Prehistory, Prehistoric age Places * AGE, the IATA airport code for Wangerooge Airfield, in Lower Saxony, Germany People * Åge, a given name * Aage, a given name * Agenore Incrocci, an Italian screenwriter Arts, entertainment, and media Fictional entities * ''Ages'', worlds in the Myst (series), ''Myst'' video game series Music * Age (song), "Age" (song), a song by Jim and Ingrid Croce Periodicals * Age ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ehud Hrushovski
Ehud Hrushovski ( he, אהוד הרושובסקי; born 30 September 1959) is a mathematical logician. He is a Merton Professor of Mathematical Logic at the University of Oxford and a Fellow of Merton College, Oxford. He was also Professor of Mathematics at the Hebrew University of Jerusalem. Early life and education Hrushovski's father, Benjamin Harshav (Hebrew: בנימין הרשב, né Hruszowski; 1928–2015), was a literary theorist, a Yiddish and Hebrew poet and a translator, professor at Yale University and Tel Aviv University in comparative literature. Ehud Hrushovski earned his PhD from the University of California, Berkeley in 1986 under Leo Harrington; his dissertation was titled ''Contributions to Stable Model Theory''. He was a professor of mathematics at the Massachusetts Institute of Technology until 1994, when he became a professor at the Hebrew University of Jerusalem. Hrushovski moved in 2017 to the University of Oxford, where he is the Merton Professor of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |