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The language of mathematics and its symbolization
Recursive construction of the relation of consequence
7 other sections not shown
a n b according assertion axiomatic axioms basic instances basic Lindenbaum algebra belong binary binary relation Boolean expressions Boolean function Boolean indeterminates classes condition construction corresponding cylindrification defined definition denote derived determined disjunction equality equivalent example exists finite sequences formal consequence formal proof formalized theory free Boolean algebra free individual indeterminates free occurrence holds homomorphism indexed Boolean algebra indexing homomorphism indexing ideal individual constant inductive assumption infinite intuitive isomorphic joins and meets laws Lemma mapping mathematical language mathematical logic mathematical theory mathematico-logical meaning metamathematical natural numbers notion obviously occur free operations order theory positive integers possible precisely predicate constants predicate logic prime ideal prime over-ideal properties propositional calculus prove quantifier quotient algebra real numbers recursive relation of consequence Remark replacement Rule satisfied Sect semantic sense sentence sentential expressions set theory set-theoretic similarly Stsf subalgebra subexpression subsets substitutively indexed algebra symbolic language symbolized mathematical syntactic valid variables