Convex algebras on an interval with semicontinuous monotone operations
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910054145327104 |
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| author | Sokolova, Ana Woracek, Harald |
| author_facet | Sokolova, Ana Woracek, Harald |
| contents | In a recent work of Matteo Mio on compact quantitative equational theories (here compact means that all its consequences are derivable by means of finite proofs) convex algebras on the carrier set [0,1] whose operations are monotone and satisfy certain semicontinuity properties occurred. We fully classify those algebraic structures by giving an explicit construction of all possible convex operations on [0,1] possessing the mentioned properties. Our result thus describes exactly the range of theories to which Mio's theorem applies. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_14955 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convex algebras on an interval with semicontinuous monotone operations Sokolova, Ana Woracek, Harald Logic in Computer Science Logic In a recent work of Matteo Mio on compact quantitative equational theories (here compact means that all its consequences are derivable by means of finite proofs) convex algebras on the carrier set [0,1] whose operations are monotone and satisfy certain semicontinuity properties occurred. We fully classify those algebraic structures by giving an explicit construction of all possible convex operations on [0,1] possessing the mentioned properties. Our result thus describes exactly the range of theories to which Mio's theorem applies. |
| title | Convex algebras on an interval with semicontinuous monotone operations |
| topic | Logic in Computer Science Logic |
| url | https://arxiv.org/abs/2603.14955 |