query: How first-order logic based ZFC can model mathematical theories formulated with higher order logic?
positive_passages.docid: 16796
positive_passages.text: Zermelo-Fraenkel set theory and Hilbert's axioms for geometry
negative_passages.docid: 96748
negative_passages.text: Formal deductions on Hilbert system
negative_passages.docid: 97187
negative_passages.text: In what formal system is Godel's Incompleteness Theorem (or similar statements of undecidability) proven?
negative_passages.docid: 42517
negative_passages.text: Is formal truth in mathematical logic a generalization of everyday, intuitive truth?
negative_passages.docid: 56191
negative_passages.text: How to demystify the axioms of propositional logic?
negative_passages.docid: 52451
negative_passages.text: Ordered Triples and Set Theory
negative_passages.docid: 96091
negative_passages.text: How does ZFC describe addition?
negative_passages.docid: 42095
negative_passages.text: Existence in ZF of a set with countable power set
negative_passages.docid: 114550
negative_passages.text: Well-ordering theorem and second-order logic
negative_passages.docid: 108533
negative_passages.text: Is there any formula of monadic second-order logic that is only satisfied by an infinite set?
negative_passages.docid: 3663
negative_passages.text: Finding counterexamples in elementary set theory.
negative_passages.docid: 97156
negative_passages.text: ZFC + $\exists$ Standard model $\rightarrow$ Con(ZFC + $\exists \omega$-model)
negative_passages.docid: 115675
negative_passages.text: Strange consequences of Axiom of Choice in Zermelo set theory
negative_passages.docid: 16187
negative_passages.text: proof of functional completeness of logical operators
negative_passages.docid: 43655
negative_passages.text: Verify is tautology by using logical equivalence
negative_passages.docid: 140868
negative_passages.text: Axiomatization of $\mathbb{Z}$ via well-ordering of positives.
negative_passages.docid: 81122
negative_passages.text: interaction between mathematical structures