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Model theory - Wikipedia
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 … 展开
This page focuses on finitary first order model theory of infinite structures.
The relative emphasis placed on the class of models of a theory as opposed to the class of definable sets within a model fluctuated in the history … 展开Definable sets
In model theory, definable sets are important objects of study. For instance, in 展开Realising and omitting types
Constructing models that realise certain types and do not realise others is an important task in model theory. Not realising a type is referred … 展开A key factor in the structure of the class of models of a first-order theory is its place in the stability hierarchy.
A complete theory T is called $${\displaystyle \lambda }$$-stable … 展开First-order logic
A first-order formula is built out of atomic formulas such as $${\displaystyle R(f(x,y),z)}$$ or $${\displaystyle y=x+1}$$ by means of the Boolean connectives $${\displaystyle \neg ,\land ,\lor ,\rightarrow }$$ 展开Basic notions
For a sequence of elements $${\displaystyle a_{1},\dots ,a_{n}}$$ of a structure $${\displaystyle {\mathcal {M}}}$$ and a subset A of $${\displaystyle {\mathcal {M}}}$$, one can consider the set of all first-order formulas 展开A theory was originally called categorical if it determines a structure up to isomorphism. It turns out that this definition is not useful, due … 展开
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Model theory - Wikipedia
A Course on Basic Model Theory | SpringerLink
网页Authors: Haimanti Sarbadhikari, Shashi Mohan Srivastava. Broadens readers understanding through its brief, lucid, and focused content on model theory. Provides a systematic approach with plenty of examples …