You can say all of those things, but they have slightly different meanings and uses: The fridge is in the kitchen: This sentence is talking about a specific fridge and a specific kitchen. It is a statement of fact. A fridge is in the kitchen: This is talking about a non-specific fridge and a specific kitchen. It is a statement of fact. It means there is a fridge in the kitchen but it's not a specific fridge. Whilst grammatically correct this sentence wouldn't commonly be used as it sounds slightly odd. You would more likely say 'There's a fridge in the kitchen'. A fridge in the kitchen: This is talking about a non-specific fridge and a specific kitchen but it isn't a complete sentence. Again, the full sentence would more likely be 'There's a fridge in the kitchen'. Or you might ask the question 'Is there a fridge in the kitchen?'. I hope that makes sense :-)

You can say: *There is A fridge in the kitchen* The best way i can explain this is that *A* is one of many, *THE* is only one. Since we only have one kitchen per home ( usually ) we use *the*.