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Why do the propositional and first-order logic systems have different choices for their domains?

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#logic #propositional-calculus #first-order-logic #model-theory
114
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Decidability of a set of universal $\mathcal{L}$-tautologies

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#logic #model-theory
403
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Is $\exists x(x=a)$ a valid formula in first order logic with equality?

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#logic #terminology #first-order-logic #predicate-logic #model-theory
122
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Is there a least standard model of Peano Arithmetics?

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#first-order-logic #model-theory #peano-axioms #nonstandard-models
722
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What are "parameters" in a formula of first-order logic?

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#logic #notation #terminology #model-theory
216
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Determining $\forall x \exists y \varphi (x,y) \to \forall y \exists x \varphi (x,y)$ is valid

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#discrete-mathematics #logic #first-order-logic #predicate-logic #model-theory
51
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What is the analogue of III.4.8 in Ebbinghaus' Mathematical Logic, for the consequence relation?

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#logic #computer-science #model-theory
151
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Cantor-Bendixson rank of isolated type

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#logic #model-theory
124
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Axiomatisation of the monadic second order theory of finite linear orders.

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#first-order-logic #order-theory #model-theory #automata #second-order-logic
127
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Finding models that realize few types

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#logic #model-theory
1.1k
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In what sense is $\sf ZFC$ "stronger" than Peano arithmetic?

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#logic #model-theory #formal-languages #provability
143
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Number of Ultrafilters on Boolean Algebra of Definable Sets (of a countable structure in a countable language)

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#first-order-logic #model-theory #boolean-algebra
314
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Characterizing worldly cardinals as the supremum (by n) of least $\Sigma_n$-extendible cardinals

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#set-theory #model-theory #large-cardinals
515
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How do "we" know the incompleteness of second-order logic?

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#logic #first-order-logic #model-theory #incompleteness #second-order-logic
83
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Weak amalgamation property for type space functors

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#model-theory

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