18956 | Asserting first-order validity implicitly involves second-order reference to classes [Putnam] |
10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
18109 | The completeness of first-order logic implies its compactness [Bostock] |
18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
19315 | In quantified language the components of complex sentences may not be sentences [Kirkham] |
17788 | First-order logic only has its main theorems because it is so weak [Mayberry] |
13624 | The 'triumph' of first-order logic may be related to logicism and the Hilbert programme, which failed [Shapiro] |
13660 | Maybe compactness, semantic effectiveness, and the Löwenheim-Skolem properties are desirable [Shapiro] |
13662 | First-order logic was an afterthought in the development of modern logic [Shapiro] |
13673 | The notion of finitude is actually built into first-order languages [Shapiro] |
10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
10986 | Not all validity is captured in first-order logic [Read] |
13534 | In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide [Wolf,RS] |
13535 | First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation [Wolf,RS] |