 About 6,360 results  books.google.com Thus, by (IX), T is a consistent extension of the essentially undecidable theory T2,
and therefore T is undecidable (cf. Theorem 3). Furthermore, every decision
procedure for T1 automatically yields a decision procedure for T. Hence T1 is ... 

 books.google.com Introduction A general method for establishing the undecidability of theories was
developed in [13]. Its basic ... There is a finitely axiomatizable and essentially
undecidable theory Q which is a fragment of the arithmetic of natural numbers.
1.2. 

 books.google.com Now we can generalize our work on undecidable theories. Hereditarily and
essentially undecidable theories A theory T is hereditarily undecidable if it is
undecidable and for every theory in the language of T, is undecidable. A theory T
is ... 

 books.google.com 1.2, If a'theory T is compatible with a finitely axiomatizable and essentially
undecidable theory 2, then T is undecidable. A still weaker fragment of number
theory, the theory R, was also introduced in [13]. R is not finitely axiomatizable.
Moreover ... 

 books.google.com by Alonzo Church in 1936; he showed that the system ofPrincipia Math ematica
is undecidable if it is wconsistent. ... The main new concept of the first part of the
book is that of a theory being essentially undecidable, which means that the ... 

 books.google.com We see thus that the equational theory of RA and all of its extensions mentioned
in (xii)(/3) are examples of equational theories that are undecidable and dually
decidable; they could be referred to as theories which are essentially dually ... 

 books.google.com (This is the case for our axioms Q, and probably for any realistic set of arithmetic
axioms.) Essential undecidability A theory is said to be essentially undecidable if
every consistent extension of it is undecidable. (By an extension of a theory T we
... 

 books.google.com Since an axiomatized theory resulting from an undecidable axiomatic theory
through omission of a finite number of ... consistent extension of Peano's number
theory is undecidable, in short that this system is essentially undecidable, we
have ... 

 books.google.com It is easy to see that any complete axiomatizable theory is decidable. The
classical result here is that any consistent theory has an extension to a complete
consistent theory. A theory is said to be essentially undecidable theory if it has no
... 

 books.google.com (c) Since T is not arithmetic it certainly is not r.e. So (T) is not a formal theory. (d)
Let (T, ) be a ... ESSENTIAL UNrfECIDABILITY Tarski calls a theory (T) essentially
undecidable iff every consistent extension of (T) is undecidable. Consider now ... 

 