I have a basic understanding of both, and intend to go into both in detail, but wanted a better idea of which is " more useful " in terms of seeing connections and understanding set theoretic things-as opposed to, say, actually proving some specific result.
12.
The intended meaning is, in gonzo set theoretic terms, " For all x, if x is an element of C, x is either an element of A or B ", or more precisely " A intersection B is the null set, and A union B is C ".
13.
D . L . Childs, Vice President of Set Theoretic Information Systems ( STIS ) Corporation, provided continuing guidance in the use of Set-Theoretic Data Structure ( STDS ) data access software for MICRO . Funding came from the Office of Manpower Administration within the U . S . Department of Labor.
14.
:The form not the content of the theories ( conversation theory and interactions of actors theory ) return to and is congruent with the forms of physical theories; such as wave particle duality ( the set theoretic unfoldment part of conversation theory is a radiation and its reception is the interpretation by the recipient of the descriptions so exchanged, and vice versa ).
15.
The usual set of axioms of set theory is called ZFC . When a set theoretic statement A is said to be equiconsistent to another B, what is being claimed is that in the metatheory ( Peano Arithmetic in this case ) it can be proven that the theories " ZFC + A " and " ZFC + B " are equiconsistent.
16.
Although, technically, there is no difference between an individual " diagram " and a " functor " or between a " scheme " and a " category ", the change in terminology reflects a change in perspective, just as in the set theoretic case : one fixes the index category, and allows the functor ( and, secondarily, the target category ) to vary.
17.
However there are many " set theoretic " statements, such as V \ cap \ mathbb { R } = L \ cap \ mathbb { R }, that can be stated ( with effort ) in second order arithmetic but are not provable even in ZFC . The best example of a theorem that is provable in ZFC but not second-order arithmetic is probably Borel determinacy . & mdash; Carl ( talk ) 23 : 15, 2 June 2009 ( UTC)
