Year: 2026
Type: article
Abstract: We show that for any class of Boolean algebras with an associative operator, if it contains the complex algebra of ( P ( N ) , ∪ ) $(\mathcal {P}(\mathbb {N}), \cup )$ left parenthesis script upper P left parenthesis double struck upper N right parenthesis comma union right parenthesis , its equational theory is undecidable. Equivalently, any associative normal modal logic valid over the frame ( P ( N ) , ∪ ) $(\mathcal {P}(\mathbb {N}), \cup )$ left parenthesis script upper P left parenthesis double struck upper N right parenthesis comma union right parenthesis is undecidable. This settles a long-open question on the decidability of hyperboolean modal logic [16], and addresses several related problems.
Source: Journal of Symbolic Logic
Author: SØREN BRINCK KNUDSTORP
Institution: University of Amsterdam
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4417538407
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