Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: As is ll known, a language of finite words, considered as labeled linear orders, is definable in monadic second-order logic (MSO) iff it is definable in the existential fragment of MSO, that is the quantifier alternation hierarchy collapses. Even more, it does not make a difference if  consider existential MSO over a linear order or a successor relation only. In this note  show that somewhat surprisingly the latter does not hold if  just add a second linear order and consider finite relational structures with two linear orders, so-called texts.
['Christian Mathissen']
I am writing a research paper on a idea Existential MSO over two successors is strictly weaker than over linear orders
[{"from": "human", "value": "I am writing a research paper on a idea Existential MSO over two successors is strictly weaker than over linear orders"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: As is ll known, a language of finite words, considered as labeled linear orders, is definable in monadic second-order logic (MSO) iff it is definable in the existential fragment of MSO, that is the quantifier alternation hierarchy collapses. Even more, it does not make a difference if  consider existential MSO over a linear order or a successor relation only. In this note  show that somewhat surprisingly the latter does not hold if  just add a second linear order and consider finite relational structures with two linear orders, so-called texts."}]