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Can I Use Functions Returning T/F in Propositional/First-Order Logic?

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#propositional-calculus #first-order-logic
46
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Can I Write Propositional Logic Statement Using Functions Returning T/F?

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#logic #propositional-calculus #predicate-logic #first-order-logic
866
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The cardinality of a language over a set of variables $V$ with $\#V= κ$

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#logic #cardinals #model-theory #first-order-logic #formal-languages
127
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Confusion with definition of $term$ in first order languages.

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#logic #predicate-logic #first-order-logic
233
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Is this set of formula consistent?

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#first-order-logic
56
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In general, how to determine the cardinality of the set of expression over a language?

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#combinatorics #logic #cardinals #first-order-logic #formal-languages
2.8k
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What is the difference between 'logical symbols' and 'relation symbols' in first order logic?

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#logic #definition #predicate-logic #first-order-logic
116
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If $T\vdash \alpha\rightarrow \Box\neg\alpha$ and $T\vdash \alpha$ then $T$ is $\omega$-inconsistent

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#first-order-logic #incompleteness
352
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Generalizing the compactness and Löwenheim-Skolem theorem

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#logic #set-theory #cardinals #model-theory #first-order-logic
97
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Formalize equivalence classes

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#logic #first-order-logic
39
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Converting statements into logical form. Am I on the right track?

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#logic #proof-verification #first-order-logic
39
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If $F(T)$ and $F(\bot)$ are tautologies is $F(Q)$ a tautology as well?

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#logic #first-order-logic
92
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Why do we have to prove the totallity of functions?

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#functions #logic #definition #first-order-logic
68
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Are these two versions of Lowenheim-Skolem equivalent?

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#logic #first-order-logic
370
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Axiomatic set theory as a first-order logic theory?

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#set-theory #first-order-logic #formal-systems

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