Order with successors is not interprétable in RCF

S. Świerczkowski

Fundamenta Mathematicae (1993)

  • Volume: 143, Issue: 3, page 281-285
  • ISSN: 0016-2736

Abstract

top
Using the monotonicity theorem of L. van den Dries for RCF-definable real functions, and a further result of that author about RCF-definable equivalence relations on ℝ, we show that the theory of order with successors is not interpretable in the theory RCF. This confirms a conjecture by J. Mycielski, P. Pudlák and A. Stern.

How to cite

top

Świerczkowski, S.. "Order with successors is not interprétable in RCF." Fundamenta Mathematicae 143.3 (1993): 281-285. <http://eudml.org/doc/212009>.

@article{Świerczkowski1993,
abstract = {Using the monotonicity theorem of L. van den Dries for RCF-definable real functions, and a further result of that author about RCF-definable equivalence relations on ℝ, we show that the theory of order with successors is not interpretable in the theory RCF. This confirms a conjecture by J. Mycielski, P. Pudlák and A. Stern.},
author = {Świerczkowski, S.},
journal = {Fundamenta Mathematicae},
keywords = {interpretation; real closed field; first-order theory of linear order; successor; real number field},
language = {eng},
number = {3},
pages = {281-285},
title = {Order with successors is not interprétable in RCF},
url = {http://eudml.org/doc/212009},
volume = {143},
year = {1993},
}

TY - JOUR
AU - Świerczkowski, S.
TI - Order with successors is not interprétable in RCF
JO - Fundamenta Mathematicae
PY - 1993
VL - 143
IS - 3
SP - 281
EP - 285
AB - Using the monotonicity theorem of L. van den Dries for RCF-definable real functions, and a further result of that author about RCF-definable equivalence relations on ℝ, we show that the theory of order with successors is not interpretable in the theory RCF. This confirms a conjecture by J. Mycielski, P. Pudlák and A. Stern.
LA - eng
KW - interpretation; real closed field; first-order theory of linear order; successor; real number field
UR - http://eudml.org/doc/212009
ER -

References

top
  1. [1] L. van den Dries, Algebraic theories with definable Skolem functions, J. Symbolic Logic 49 (1984), 625-629. Zbl0596.03032
  2. [2] L. van den Dries, Definable sets in O-minimal structures, lecture notes at the University of Konstanz, spring 1985. 
  3. [3] L. van den Dries, Tame Topology and O-minimal Structures, book in preparation. 
  4. [4] J. Krajíček, Some theorems on the lattice of local interpretability types, Z. Math. Logik Grundlag. Math. 31 (1985), 449-460. Zbl0559.03034
  5. [5] J. Mycielski, A lattice connected with relative interpretability of theories, J. Symbolic Logic 42 (1977), 297-305. Zbl0371.02026
  6. [6] J. Mycielski, P. Pudlák and A. Stern, A lattice of chapters of mathematics, Mem. Amer. Math. Soc. 426 (1991). Zbl0696.03030
  7. [7] A. Pillay and C. Steinhorn, Definable sets in ordered structures I, Trans. Amer. Math. Soc. 295 (1986), 565-592. Zbl0662.03023
  8. [8] A. Stern, The lattice of local interpretability of theories, Ph.D. Thesis, University of California, Berkeley, March 1984. 
  9. [9] A. Stern and S. Świerczkowski, A class of connected theories of order, J. Symbolic Logic, to appear. Zbl0805.03048

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.