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Interpreting statements as conditional vs conjunction in discrete mathematics

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#discrete-mathematics #logic #predicate-logic #first-order-logic #quantifiers
96
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Class $K^{\infty}$ is elementary provided that $K$ is.

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#logic #model-theory #first-order-logic
416
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If $\Phi$ has only finite models, there is some $n\in \mathbb{N}$ such that each model has at most $n$ elements.

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#logic #proof-verification #model-theory #first-order-logic
49
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How is $\Phi^{\vdash}_{PA} \subset Th(R)$?

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#number-theory #logic #first-order-logic
117
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Prove a first-order theory is complete if given $\vdash P\lor Q$ we have $\vdash P$ or $\vdash Q$

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#logic #first-order-logic
221
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Turning statement into predicate logic

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#logic #predicate-logic #first-order-logic #logic-translation
419
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Are there new statement at every stage of the arithmetical hierarchy?

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#logic #first-order-logic #computability
123
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Sets of sentences-Structures-Definable subsets in a structure

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#logic #model-theory #first-order-logic
286
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Model-completeness without quantifier elimination

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#model-theory #first-order-logic
338
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Incomplete, model-complete theories

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#model-theory #first-order-logic
317
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Incomplete countable theory T

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#logic #model-theory #first-order-logic
88
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Quantitive compactness theorem, getting explicit bounds

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#logic #model-theory #first-order-logic
97
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How do I show that $(A \cup B) \times C = (A \times C) \cup (B \times C)$ holds for all sets $A$, $B$, and $C$ using mathematical logic?

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#elementary-set-theory #logic #predicate-logic #first-order-logic
264
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First Order Logic - Formalization and Correctness

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#logic #predicate-logic #first-order-logic
45
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First order logic - Translating from spoken word to logic syntax and simple proof

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#first-order-logic #logic-translation

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