9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
13544 | Inconsistency or entailment just from functors and quantifiers is finitely based, if compact [Bostock] |
13618 | Compactness means an infinity of sequents on the left will add nothing new [Bostock] |
13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
10287 | If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W] |
13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
17789 | No logic which can axiomatise arithmetic can be compact or complete [Mayberry] |
13630 | Non-compactness is a strength of second-order logic, enabling characterisation of infinite structures [Shapiro] |
13646 | Compactness is derived from soundness and completeness [Shapiro] |
13699 | Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider] |
10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
10975 | Compactness does not deny that an inference can have infinitely many premisses [Read] |
10976 | Compactness makes consequence manageable, but restricts expressive power [Read] |
10977 | Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read] |
17867 | If a concept is not compact, it will not be presentable to finite minds [Almog] |