Paragraded Structures Inspired By Mathematical Logic
DOI:
https://doi.org/10.5644/SJM.12.3.06Keywords:
Paragraded structures, elementary chains, bi-emeddabilityAbstract
We use methods from mathematical logic to give new examples of paragraded structures, showing that at certain cardinals all first order structures are paragraded. We introduce the notion of biembeddability to measure when two paragraded structures are basically the same. We prove that the bi-embeddability of the paragraduating system gives rise to the bi-embeddability of the limiting structures. Under certain circumstances the converse is also true, as we show here. Finally, we show that one paragraded structure can have many graded substructures, to the extent that the number of the same is not always decidable by the axioms of set theory.
* This paper was presented at the International Scientific Conference Graded structures in algebra and their applications, dedicated to the memory of Prof. Marc Krasner, IUCDubrovnik, Croatia, September, 22-24, 2016.
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References
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