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Ω-consistent theory

In mathematical logic, an ω-consistent (or omega-consistent, or numerically segregative) theory is a theory (collection of sentences) that is not only (syntactically) consistent (that is, does not prove a contradiction), but also avoids proving certain infinite combinations of sentences that are intuitively contradictory. The name is due to Kurt Gödel…

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Ω-logic

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Ω-consistent theory

Nodes43
Edges42
Triples6
Avg. degree1.95
Density0.046512
Components1

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Important terminology

theory pa model natural language ω-consistent ω-logic arithmetic numbers proves number consistent every con ω-inconsistent sound displaystyle predicate also gödel

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
0instance ofor constant terms0.80text
1instance ofor constant terms0.80text
Peano arithmeticinstance ofmeaning one with intended domain the natural numbers0.80text
the predicate N is redundantinstance ofmeaning one with intended domain the natural numbers0.80text
may be omitted from the languageinstance ofmeaning one with intended domain the natural numbers0.80text
with the consequent of the rule for each P simplifying toinstance ofmeaning one with intended domain the natural numbers0.80text

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