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Can there be a consistent strong effectively generated first order theory that is complete for all sentences of its language up to a specific length?

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#logic #first-order-logic #incompleteness
48
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Using recursion theory to show a particular sentence is not provable in an extension of PA.

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#logic #recursion #proof-theory #incompleteness
94
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When does a formal system cease to be able to be complete and consistent?

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#incompleteness #formal-systems
742
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What is a valid function definition?

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#functions #logic #natural-numbers #incompleteness
122
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Rosser's trick practice exam question

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#computability #solution-verification #incompleteness
235
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Proof of Gödel's Incompleteness Theorem by modal logic

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#incompleteness #modal-logic
197
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Does $\omega$-consistency of ZF imply $\omega$-consistency of ZFC

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#logic #set-theory #model-theory #incompleteness
78
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Completeness of Logic versus completeness of a theory

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#logic #first-order-logic #predicate-logic #incompleteness
222
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Quantifying the "Complexity" or "Strength" of Axiomatic Systems

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#axioms #turing-machines #incompleteness
261
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False Σ1-sound theories

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#logic #set-theory #incompleteness
216
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Why can't we prove the consistency of ZFC by proving its axioms is satisfiable?

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#elementary-set-theory #logic #incompleteness
79
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Consistency hierarchies and Gödel’s theorem

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#incompleteness
763
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If a system is complete, must it be inconsistent?

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#incompleteness
320
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Gödel's Incompleteness Theorem and the Millennial Problems

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#logic #incompleteness
254
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A finitist Gödel second incompleteness theorem

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#logic #set-theory #incompleteness #meta-math

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