Title :
McColm´s conjecture [positive elementary inductions]
Author :
Gurevich, Yuri ; Immerman, Neil ; Shelah, Saharon
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., Michigan Univ., Ann Arbor, MI, USA
Abstract :
G. McColm (1990) conjectured that positive elementary inductions are bounded in a class K of finite structures if every (FO+LFP) formula is equivalent to a first-order formula in K. Here (FO+LFP) is the extension of first-order logic with the least fixed point operator. We disprove the conjecture. Our main results are two model-theoretic constructions, one deterministic and the other randomized, each of which refutes McColm´s conjecture
Keywords :
formal logic; finite structures; first-order formula; first-order logic; least fixed point operator; model-theoretic constructions; positive elementary inductions; Building materials; Computer science; Logic; Mathematics; Vocabulary;
Conference_Titel :
Logic in Computer Science, 1994. LICS '94. Proceedings., Symposium on
Conference_Location :
Paris
Print_ISBN :
0-8186-6310-3
DOI :
10.1109/LICS.1994.316091
