I looked on the web to search for weakly compact cardinals.
 The web sources indicate many properties of weakly compact cardinals and say that their existence is not entailed by the axioms of ZFC. However it is not indicated whether their existence is {\it consistent} with the axioms of ZFC.


So my question is: Is it known that the axiom of existence of weakly compact cardinals consistent with ZFC?


Thanks



Existence of weakly compact cardinals
As weakly compact cardinals are in particular [(strongly) inaccessible](http://en.wikipedia.org/wiki/Inaccessible_cardinal), it follows from Gödel's Second Incompleteness Theorem that ZFC cannot prove the implication "Con(ZFC) implies Con (ZFC + $\exists$weakly-compact )." (Unless, of course, if ZFC is itself inconsistent, at which point this is all a lot of bunk).


(The linked Wikipedia article outlines the basic reasoning.)


Any argument for the consistency of "ZFC + $\exists$weakly-inaccessible" must therefore transcend ZFC. (But, as mentioned by Asaf, no contradictions have been found thus far been under the assumption of the existence of weakly-compact cardinals.)


