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A new method for undecidability proofs of first order theories

Ralf Treinen
1992 Journal of symbolic computation  
First it proposes a general methodology for proving results of the kind : The first order theory of the predicate logic model I = . . . is undecidable .  ...  We claim that the reduction of Post's Correspondence Problem to the decision problem of a theory provides a useful tool for proving undecidability of first order theories given by some interpretation.  ...  A New Method for Undecidability Proofs of First Order Theories RALF TREINEN DFKI, Stuhlsatzenhausweg S, W6600 Saarbrucken Germany (Received 21 March 1991) We claim that the reduction of Post's Correspondence  ... 
doi:10.1016/0747-7171(92)90016-w fatcat:ddhabjmntfh2jg7c2l2hdyeen4

A new method for undecidability proofs of first order theories [chapter]

Ralf Treinen
1990 Lecture Notes in Computer Science  
First it proposes a general methodology for proving results of the kind : The first order theory of the predicate logic model I = . . . is undecidable .  ...  We claim that the reduction of Post's Correspondence Problem to the decision problem of a theory provides a useful tool for proving undecidability of first order theories given by some interpretation.  ...  A New Method for Undecidability Proofs of First Order Theories RALF TREINEN DFKI, Stuhlsatzenhausweg S, W6600 Saarbrucken Germany (Received 21 March 1991) We claim that the reduction of Post's Correspondence  ... 
doi:10.1007/3-540-53487-3_34 fatcat:prtpemxjtfhmboysjagpajngxm

Page 6087 of Mathematical Reviews Vol. , Issue 87k [page]

1987 Mathematical Reviews  
The method of proof is as follows. First an observation of Jensen is applied to deduce a weak form of the square principle from the existence of a A*-special Aronszajn tree.  ...  A previous paper of the author {same journal 32 (1986), no. 1, 29-44; MR 87i:03108] gave a new first-order axiomatization of H. M.  ... 

Undecidability of free pseudocomplemented semilattices

PawełM. Idziak
1987 Publications of the Research Institute for Mathematical Sciences  
Decision problem for the first order theory of free objects in equational classes of algebras was investigated for groups (Malcev [10]), semigroups (Quine [12]), commutative semigroups (Mostowski [11])  ...  For Sen let 33 5 denote the pcs obtained from the lattice 2 s of all subsets of S by adjoining a new smallest element 0 5 .  ...  He would like to thank Professor Hiroakira Ono for his hospitality,  ... 
doi:10.2977/prims/1195176449 fatcat:j7zjypqjffg4lm4pqdjl7qhwcy

Undecidability, unit groups, and some totally imaginary infinite extensions of Q [article]

Caleb Springer
2020 arXiv   pre-print
We produce new examples of totally imaginary infinite extensions of Q which have undecidable first-order theory by generalizing the methods used by Martinez-Ranero, Utreras and Videla for Q^(2).  ...  This proves the undecidability of Q^(d)_ab for all d ≥ 2.  ...  Clearly, if O L is definable in L and the first-order theory of O L is undecidable, then the first-order theory of L is also undecidable.  ... 
arXiv:1910.01239v2 fatcat:v4sg5twlendnll3keyww2a2eti

Eleventh Meeting of the Association for Symbolic Logic

1949 Journal of Symbolic Logic (JSL)  
A new mathematical proof for a variant of transfinite induction up to the first epsilonnumber is given. The proof is (i) capable of generalization, (ii) of metamathematical interest. 16. C D .  ...  calculi of first order.  ... 
doi:10.2307/2269014 fatcat:s3ypqzvva5cp3dmqc5qawlmsqq

Page 8474 of Mathematical Reviews Vol. , Issue 2004k [page]

2004 Mathematical Reviews  
The same holds for the first-order logic of proofs with monotonicity axiom QLP®.  ...  The proof of the upper bound shows the standard methods of infinitary proof theory at work.  ... 

On 2nd order intuitionistic propositional calculus with full comprehension

Dov M. Gabbay
1974 Archive for Mathematical Logic  
The proof of undecidability uses the same method introduced in Gabbay [3, 4] and used to obtain undecidability results for a large class of intuitionistic theories.  ...  Kit Fine has obtained undecidability results for 2nd order modal logics.  ... 
doi:10.1007/bf02015377 fatcat:pndaucaiv5bjfkjubqj3l2bj2i

Decidable and undecidable logics with a binary modality

�gnes Kurucz, Istv�n N�meti, Ildik� Sain, Andr�s Simon
1995 Journal of Logic, Language and Information  
is on those parts of the proof methods which have been well known for the specialists.  ...  We put an emphasis on the demonstration of proof-techniques, and hope that this will also help in finding the borderlines between decidable and undecidable fragments of usual first-order logic.  ...  We are especially grateful to Steven Givant for extensive help.  ... 
doi:10.1007/bf01049412 fatcat:ggzx4o3opbhqni6wbnhhpceeaa

Alfred Tarski and undecidable theories

George F. McNulty
1986 Journal of Symbolic Logic (JSL)  
We will say that a set of elementary sentences is a theory provided it is closed with respect to logical consequence and we will say that a theory is decidable or undecidable depending on whether it is  ...  Tarski's work on decidability falls into four broad areas: elementary theories which are decidable, elementary theories which are undecidable, the undecidability of theories of various restricted kinds  ...  Perhaps Tarski's most far-reaching contribution to our understanding of undecidable theories is the paper A general method in proofs of undecidability, which is the first of the three papers that comprise  ... 
doi:10.2307/2273902 fatcat:iav44bpgjrgztkhoxpotrfruge

New formally undecidable propositions: non-trivial lower bounds on proof complexity and related theorems

H. Luckhardt
1991 Theoretical Computer Science  
Thus we have a new large class of formally undecidable mathematical propositions.  ...  This is new evidence for the validity of Cook's conjecture.  ...  I VY,, %I + G for first order G. We can take F* to be a sequence of such first order approximations to F.  ... 
doi:10.1016/0304-3975(91)90272-4 fatcat:sxrrh4cxefhknccipacsn4r3nu

Page 750 of Mathematical Reviews Vol. 55, Issue 3 [page]

1978 Mathematical Reviews  
Logik Grundlagen Math. 14 (1968), 457-472; MR 38 #5620] showed that the first order theory of 2 is undecidable, and his proof shows that the degree of this theory is at least 0’.  ...  The author gives a new method of constructing initial segments of degrees of order type w based on the idea of iterated forcing.  ... 

A Proof of Syntactic Incompleteness of the Second-Order Categorical Arithmetic

Giuseppe Raguní
2017 OALib  
Nor is it legitimate to assert that the undecidability of the statements is generally kept in passing from a certain theory (such as PA) to another that includes it (such as AR).  ...  Pending a response to the previous question, this paper aims to present a proof of the syntactic/semantical incompleteness of AR, by examples based on the different modes of representation (i.e. codes)  ...  Here the Gödel's famous statement (G), undecidable in PA, still means "no gödelian code of a proof of myself exists" but no longer "I'm not a theorem", since not every proof has a gödelian code (those  ... 
doi:10.4236/oalib.1103969 fatcat:fbsqz43skvgjhn3nvpi2rlzcwi

Page 6434 of Mathematical Reviews Vol. , Issue 96k [page]

1996 Mathematical Reviews  
As an application, he proves hereditary undecidability for £,-theories of some natural classes of finite structures, such as graphs, lattices, and partial orders, as well as natural structures arising  ...  The new metatheorem grew, in part, out of an effort to find a new proof of Ash’s metatheorem. The new metatheorem yields the one in [C. J. Ash, op. cit; MR 91g:03090], and it seems more flexible.  ... 

Definability and decidability for rings of integers in totally imaginary fields [article]

Caleb Springer
2022 arXiv   pre-print
This implies that the ring of integers of ℚ^tr(i) is undecidable and first-order non-definable in ℚ^tr(i).  ...  More generally, when L is a totally imaginary quadratic extension of a totally real field K, we use the unit groups R^× of orders R⊆𝒪_L to produce existentially definable totally real subsets X⊆𝒪_L.  ...  Namely, in the context of Theorem 3.4, if the existential or first order theory of OK is undecidable then the same is true for OL .  ... 
arXiv:2207.00140v1 fatcat:eu5bxn32end7pnyshma66pgueu
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