[[Category:Logic and foundations]]
58 bytes (6 words) - 16:41, 2 April 2018
...rom the classical one, e.g. [[Modal logic|modal logic]], or intuitionistic logic if the meta-theory is built within the frame of [[Intuitionism|intuitionism
....g. by means of set theory. In this case, classical logic acts as the meta-logic.
1 KB (157 words) - 17:10, 7 February 2011
...lign="top"> R. Fraïssé, ''Theory of Relations'', Studies in Logic and the Foundations of Mathematics, Elsevier (2011) {{ISBN|0080960413}}</TD></TR>
[[Category:Logic and foundations]]
826 bytes (126 words) - 19:34, 17 November 2023
...ishment of derivability. One of the most important results in mathematical logic is the theorem stating that the cut rule is sound (see [[Gentzen formal sys
...matical principles such as consistency, $\omega$-consistency, completeness and reflection principles.
1 KB (207 words) - 19:21, 17 October 2014
...uccessful. As K. Gödel showed [[#References|[3]]], no formalized system of logic can be an adequate basis for mathematics (cf. [[Gödel incompleteness theor
...align="top">[5]</TD> <TD valign="top"> A.A. Fraenkel, Y. Bar-Hillel, "Foundations of set theory" , North-Holland (1958)</TD></TR></table>
3 KB (445 words) - 17:13, 7 February 2011
...ssing an object of the theory and depending on parameters $x_1,\dots,x_n$ (and possibly also on other parameters), then
...op">[2]</TD> <TD valign="top"> H.B. Curry, "Foundations of mathematical logic" , McGraw-Hill (1963)</TD></TR></table>
1 KB (214 words) - 17:18, 14 February 2020
''in mathematical logic''
...the consistency of the axiom of choice can be regarded as the syntactical and finitistically-provable assertion that if the Zermelo–Fraenkel formal the
2 KB (328 words) - 17:25, 7 February 2011
A program for the foundations of mathematics initiated by D. Hilbert. The aim of this program was to prov
...ssertions of the theory are changed to finite sequences of definite signs, and the logical methods of inference — to formal rules for generating new for
3 KB (387 words) - 17:16, 7 February 2011
...place predicate symbol, i.e. a subset of the Cartesian power $M^n$ of $M$, and an $n$-place function $M^n\to M$ to an $n$-place function symbol. The set $
<TR><TD valign="top">[1]</TD> <TD valign="top"> S.C. Kleene, "Mathematical logic" , Wiley (1967)</TD></TR>
1 KB (219 words) - 10:43, 18 October 2016
...y representatives of the intuitionistic and constructive directions in the foundations of mathematics (cf. [[Intuitionism|Intuitionism]]; [[Constructive mathemati
1 KB (158 words) - 12:49, 17 March 2014
* R. Fraïssé, ''Theory of Relations'', Studies in Logic and the Foundations of Mathematics, Elsevier (2011) p.44. {{ISBN|0080960413}}
451 bytes (77 words) - 20:25, 20 November 2023
...et of truth values (cf. [[Truth value|Truth value]]) $\{\text T,\text F\}$ and taking values in this set. With every [[Logical operation|logical operation
...in the set $\{\text T,\text F\}$. Such functions are used in mathematical logic as an analogue of the concept of a [[Predicate|predicate]].
806 bytes (143 words) - 16:55, 2 November 2014
[[Category:Logic and foundations]]
619 bytes (104 words) - 18:49, 19 October 2014
...hus, if $f$ is a variable with as values integrable real-valued functions, and $x$, $a$, $b$ are variables whose values are real numbers, then the express
...ules, independent of the semantics of the language, for constructing terms and distinguishing free variables in them. In many-sorted languages there are a
1 KB (225 words) - 22:30, 2 November 2014
* Peter T. Johnstone; ''Sketches of an elephant'', ser. Oxford Logic Guides (2002) Oxford University Press. {{ISBN|0198534256}} pp. 491-492 {{
...en; ''Categorical Foundations: Special Topics in Order, Topology, Algebra, and Sheaf Theory'', (2004) Cambridge University Press {{ISBN|0-521-83414
1 KB (198 words) - 16:50, 4 November 2023
A methodological point of view, due to D. Hilbert, as to what objects and methods of argument in mathematics should be counted as absolutely reliable
...xample the written form of natural numbers, formulas in symbolic language, and finite collections of them;
2 KB (370 words) - 12:35, 17 March 2014
[[Category:Logic and foundations]]
854 bytes (130 words) - 19:13, 17 October 2014
...he equation $x+3=2$", then one is using $x$ as the name of the letter $x$, and is using "$x+3=2$" as the name of the expression $x+3=2$. If one says "12
...the meaning of the term with the term itself: it is both the object itself and the name by which it is denoted.
2 KB (318 words) - 14:25, 30 December 2018
Please remove this comment and the {{TEX|auto}} line below,
and $ {} _ {-} ^ {*} $,
3 KB (468 words) - 06:29, 30 May 2020
...general scheme: After an alphabet $A$ not containing the letter $\bullet$ and a natural number $l$ have been selected, a derivation rule with $l$-premise
.../TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> J.B. Rosser, "Logic for mathematicians" , McGraw-Hill (1953)</TD></TR></table>
3 KB (431 words) - 19:19, 17 October 2014