Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Paradox regained: Life beyond Goedel's shadow   Goedel's explicit thesis was that his undecidable formula GUS is a
well-formed, well-defined formal sentence in any formalisation of Intuitive
Arithmetic IA in which the axioms and rules of inference are recursively
definable. His implicit thesis was that GUS is not formally inconsistent in any
such system.
  I argue in a constructive, intuitionistically unobjectionable, and
recursively definable formalisation PP of IA that GUS is a well-formed formula
but an ill-defined formal sentence reflecting the "Liar" paradox in PP.
  Further, introducing "formal truth" and "provability" values to selected
propositions of IA through PP leads to the collapse of Lucas' Goedelian
argument.

3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an