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Results tagged with lo.logic
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user 156547
first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
5
votes
0
answers
64
views
Definable pseudo-standard predicates in Internal Set Theory
Consider the usual language $\mathcal{L}=(\in, \mathrm{st})$ of Nelson's Internal Set Theory, and a unary $\mathcal{L}$-predicate $P$. For an $\mathcal{L}$-formula $\varphi$, let $\varphi^P$ denote th …
- 756
6
votes
1
answer
255
views
Existence property for second-order propositional logic
Consider the intuitionistic second-order propositional calculus (SOL) formulated in the full $\wedge,\vee,\rightarrow,\bot,\top,\forall,\exists$ language.
Question: Assume that $\Gamma$ and $\Psi$ are …
- 756
9
votes
2
answers
373
views
How big can function spaces get without extensionality?
In what follows we work in the usual formulation of Martin-Löf Type Theory including Axiom K [1]. Boldface numbers $\mathbf{n}$ denote the usual finite type with $n$ elements.
Motivation
Postulating f …
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