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Some of the things I've learned every day since Oct 10, 2016Thu, 19 Oct 2017 07:24:22 +0000hourly1http://wordpress.com/Comment on 172: Infinite Models of L-Theories (Variation of Lowenheim-Skolem) by 173: Vaught’s Test | Today I Learned
https://zwaltman.wordpress.com/2017/10/18/172-infinite-models-of-l-theories-variation-of-lowenheim-skolem/comment-page-1/#comment-87
Thu, 19 Oct 2017 07:24:22 +0000http://zwaltman.wordpress.com/?p=3238#comment-87[…] , meaning are satisfiable, meaning both have infinite models (since has no finite models), so by [172] we can find models of cardinality which respectively satisfy these theories. But since disagree […]

]]>Comment on 141: Isomorphisms and Elementary Equivalence (Model Theory) by 166: Elementary Equivalence and Isomorphism between Finite Structures | Today I Learned
https://zwaltman.wordpress.com/2017/09/10/141/comment-page-1/#comment-81
Wed, 11 Oct 2017 02:56:25 +0000http://zwaltman.wordpress.com/?p=2591#comment-81[…] be a first-order language. In general, it is true that if two -structures are isomorphic, then they are elementarily equivalent. […]

]]>Comment on 151: Henkin Witness (Logic) by 165: The Compactness Theorem (Henkin Construction) | Today I Learned
https://zwaltman.wordpress.com/2017/09/25/151-henkin-witness-logic/comment-page-1/#comment-80
Tue, 10 Oct 2017 04:25:17 +0000http://zwaltman.wordpress.com/?p=2767#comment-80[…] construct a language and a finitely-satisfiable -theory such that any -theory extending has the witness property. The way we do this is by first adding a constant symbol to for each -formula with a single free […]

]]>Comment on 152: The Compactness Theorem by 165: The Compactness Theorem (Henkin Construction) | Today I Learned
https://zwaltman.wordpress.com/2017/09/26/152-the-compactness-theorem/comment-page-1/#comment-79
Tue, 10 Oct 2017 04:25:15 +0000http://zwaltman.wordpress.com/?p=2788#comment-79[…] logic, the Compactness Theorem states that a first-order theory is satisfiable if and only if it is finitely satisfiable. Here we […]

]]>Comment on 153: Sufficient Condition for Existence of Primitive of Complex Function by Morera’s Theorem | Today I Learned
https://zwaltman.wordpress.com/2017/09/27/153-sufficient-condition-for-existence-of-primitive-of-complex-function/comment-page-1/#comment-71
Wed, 27 Sep 2017 22:52:13 +0000http://zwaltman.wordpress.com/?p=2804#comment-71[…] is an immediate corollary to the observation in [153], since if is a primitive of on then itself is holomorphic on […]

]]>Comment on 136: The Reimann Sphere by 138: Projected Circles on the Reimann Sphere | Today I Learned
https://zwaltman.wordpress.com/2017/09/05/136-the-reimann-sphere/comment-page-1/#comment-62
Thu, 07 Sep 2017 08:03:32 +0000http://zwaltman.wordpress.com/?p=2488#comment-62[…] the Reimann Sphere projection, circles on the sphere are mapped to “circles” in the extended complex plane […]

]]>Comment on 123: Skip Lists (Intro) by 124: Skip List Search Algorithm | Today I Learned
https://zwaltman.wordpress.com/2017/07/25/123-skip-lists-intro/comment-page-1/#comment-57
Thu, 27 Jul 2017 07:37:06 +0000http://zwaltman.wordpress.com/?p=2257#comment-57[…] The following is an informal description of the algorithm for searching for an element in a skip list: […]

]]>Comment on 120: Z Order by 121: Another Description of Z Order | Today I Learned
https://zwaltman.wordpress.com/2017/07/22/120-z-order/comment-page-1/#comment-56
Sun, 23 Jul 2017 09:14:26 +0000http://zwaltman.wordpress.com/?p=2154#comment-56[…] clear description of Z Order, equivalent to the binary description, comes from depth-first traversal of a […]