metamathematical

Hilbert and his school, with Bernays, Ackermann and von Neumann as foremost, as well as young Herbrand in France, pursued the metamathematical study of arithmetic in the latter part of the 1920s.

Chores 2009

This was before his metamathematical program for the development of a proof theory emerged.

Chores 2009

Together, these four responses to Russell's paradox have helped logicians develop an explicit awareness of the nature of formal systems and of the kinds of metalogical and metamathematical results commonly associated with them today.

Russell's Paradox Irvine, A. D. 2009

One can well enough see either side of this metaphysical or metamathematical debate.

Chatting Theology with Robert Novak Sean 2008

The very definition of a category evolved over time, according to the author's chosen goals and metamathematical framework.

Category Theory Marquis, Jean-Pierre 2007

These frameworks arose both as attempts to recover the simplicity of the type-free approach, as derived from the so-called naive comprehension principle, as well as in order to satisfy metamathematical needs, such as the clarification of fundamental concepts underlying the notions of

Paradoxes and Contemporary Logic Cantini, Andrea 2007

Kurt Friedrich Gödel (b. 1906, d. 1978), "established, beyond comparison, as the most important logician of our times," in the words of Solomon Feferman (Feferman 1986), founded the modern, metamathematical era in mathematical logic.

Kurt Gödel Kennedy, Juliette 2007

In a nutshell: paradoxes tell us that we must develop a metamathematical analysis of the notions of proof and of the axiomatic method; their importance is methodological as well as epistemological.

Paradoxes and Contemporary Logic Cantini, Andrea 2007

Finsler 1926 applies Richard's paradox in order to produce metamathematical results, in particular ˜formally undecidable propositions™.

Paradoxes and Contemporary Logic Cantini, Andrea 2007

With the work of Gödel and Tarski, paradoxical arguments were reshaped into fixed point results, while the semantic conception of truth, the formalization of semantics and the arithmetization of syntax yielded firm grounds for systematic metamathematical investigations.

Paradoxes and Contemporary Logic Cantini, Andrea 2007