axiomatized

What Gödel showed is that, for any consistent, recursively axiomatized formal system, F, strong enough for arithmetic, there are truths expressible in purely arithmetical language which are not provable in F.

Non-Deductive Methods in Mathematics Baker, Alan 2009

There's a technical solution to Skolem's Paradox which explains why the Löwenheim-Skolem Theorems pose no problems for either naive forms of set-theoretic realism or various forms of axiomatized set theory.

Skolem's Paradox Bays, Timothy 2009

˜Ïƒ™ in place of set abstraction, it follows that the parthood relation axiomatized by GEM has essentially the same properties as the inclusion relation in standard set theory.

Wild Dreams Of Reality, 3 2009

For Hilbert on the other hand, at least in the context of axiomatized geometry, the logical relations simply are the formally-describable relations, since they have entirely to do with the structure exhibited by the sentences in question, or equivalently with the

The Frege-Hilbert Controversy Blanchette, Patricia 2009

It's important to emphasize that this analysis also explains why Skolem's Paradox doesn't introduce contradictions into various forms of axiomatized set theory, even when these axiomatizations are themselves understood formalistically or model-theoretically.

Skolem's Paradox Bays, Timothy 2009

Aristotle's account of proof as demonstrative argument fits very well to the structure of ancient geometry as axiomatized in Euclid.

Chores 2009

Given this, our only real option is to fall back on some form of axiomatized set theory, and the only respectable way to understand our axioms is algebraically (since understanding them intuitively would amount to falling back into our previously discredited naiveté).

Skolem's Paradox Bays, Timothy 2009

D-complete, that is, they all may be axiomatized by axioms and the rule of condensed detachment.

Combinatory Logic Bimbó, Katalin 2008

Economic theories have been axiomatized, and articles and books of economics are full of theorems.

Philosophy of Economics Hausman, Daniel M. 2008

The Nagel-Schaffner approach to theory reduction assumes a syntactic account of theory structure such that they are axiomatized systems formalizable in first order predicate calculus.

Reductionism in Biology Brigandt, Ingo 2008