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| Title of object: |
topic entry on foundations of mathematics |
| Canonical Name: |
TopicEntryOnFoundationsOfMathematics |
| Type: |
Topic |
| Created on: |
2008-04-20 13:43:54 |
| Modified on: |
2008-07-21 06:14:11 |
| Classification: |
msc:03-00 |
| Keywords: |
Mathematical Foundations: Axioms, Structures and Logics, Symbolic and Quantum Computations, Algebraic Topology, Abelian and Non-Abelian theories and structures, generalized theorems, Model and Proof theories |
| Defines: |
the `essential` Mathematics, Computation Methods, Proofs, Models, Fundamental Mathematical Concepts, Adjointness in Foundations, Galois theories |
| Synonyms: |
topic entry on foundations of mathematics=Mathematical Foundations: Axioms
topic entry on foundations of mathematics=Structures and Logics |
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Content:
This is an entry-in-progress for a new topic entry on the foundations of mathematics.
\begin{enumerate}
\item Axiomatic Foundations
\item Adjointness, Equivalence, Isomorphism and the Foundation of Mathematics
\item Syntax and semantics
\item Set theory and Classes
\item Concepts in set theory
\item Index of set theory
\item Logic and Axiomatic theories
\item Logic categorical algebras: Post, \L{}ukasiewicz and $MV$ logics
\item Algebraic topology and Algebraic geometry
\item AQFT
\item Abstract and Unviversal algebras
\item Abstract Relational theories
\item Homological algebra
\item Category theory
\item Abelian structures and theories
\item Categories of logic algebras
\item Functor categories and super-categories
\item Index of category theory
\item Topoi and extended toposes
\item Supercategories and higher dimensional algebra
\item Non-Abelian structures and theories
\item Non-Abelian Algebraic Topology
\item Classical and categorical Galois theories
\item Model theory
\item Proof theory: from axioms to results
\item Symbolic computation
\item Theory of computation
\item Measure theory
\item Representation theory
\end{enumerate}
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